CDO Pricing: Binomial Expansion Technique
BET is a relatively simple technique used by Moody's to price and rate CDOs.
- First, the collateral pool is mapped to a hypothetical portfolio of N uncorrelated assets (the diversity score).
- The default probability of assets in the hypothetical portfolio is then calculated with WARF (Weighted Average Rating Factor) .
- Since the default event of each asset is uncorrelated, the probability of J defaults in the portfolio simply follows binomial distribution:
(DS: diversity score. PD: probability of default for each asset)
- With this distribution, the expected loss (EL) for each CDO tranche can now be calculated:
(Lj: loss for a given tranche with J defaults)
- The expected loss can now be used to price or rate the CDO tranche by referencing comparable securities (i.e. with similar default probability).
The BET methodology gives a sneak preview of what's deep down in the CDO pricing rabbit hole without getting into the rocket sciences (Monte Carlo, Copula, etc). Here is a good paper that compares the BET with Monte Carlo simulations.
